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General Quantitative Genetic Methods for Comparative Biology

  • Chapter
Modern Phylogenetic Comparative Methods and Their Application in Evolutionary Biology

Abstract

There is much in common between the aim and tools of the quantitative geneticist and the comparative biologist. One of the most interesting statistical tools of the quantitative genetics (QG) is the mixed model framework, especially the so-called animal model, which can be used for comparative analyses. In this chapter, we describe the phylogenetic generalised linear mixed model (PGLMM), which encompasses phylogenetic (linear) mixed model (PMM). The widely used phylogenetic generalised least square (PGLS) can be seen as a special case of PGLMM. Thus, we demonstrate how PGLMM can be a useful extension of PGLS, hence a useful tool for the comparative biologist. In particular, we show how the PGLMM can tackle issues such as (1) intraspecific variance inference, (2) phylogenetic meta-analysis, (3) non-Gaussian traits analysis, and (4) missing values and data augmentation. Further possible extensions of the PGLMM and applications to phylogenetic comparative (PC) analysis are discussed at the end of the chapter. We provide working examples, using the R package MCMCglmm, in the online practical material (OPM).

The original version of this chapter was revised: Online Practical Material website has been updated. The erratum to this chapter is available at https://doi.org/10.1007/978-3-662-43550-2_23

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Notes

  1. 1.

    But, any kind of evolutionary model yielding such a variance–covariance matrix can be used, such as Martins and Hansen’s (1997) or ACDC processes (Blomberg et al. 2003). In practice, parameters of such models would be inferred before using the mixed model, but nothing, in theory, forbids the construction of a complex mixed model inferring these components along with performing the comparative regression.

  2. 2.

    Of course, there can be an arbitrary number of such co-factors (either continuous or categorical variables).

  3. 3.

    Note that, although \( \lambda \) could be forced to one by setting up \( \sigma^{2}_{R} = 0 \) in the model, this could cause numerical instability in frequentist software or strong auto-correlation in MCMC algorithms. The software MCMCglmm, for example, does not allow such a setting. Furthermore, there is some relevance in assuming that some of the biological variability is not captured by the phylogeny (such as environment or even measurement variability), hence assuming a residual variance. Also, notably, when \( \sigma^{2}_{R} = 0 \), PMM can be seen as equivalent to PGLS and thus PIC (Stone et al. 2011; Blomberg et al. 2012).

  4. 4.

    This is not totally true, since \( \sigma^{2}_{R} \) also include noise such as measurement error, which is very difficult to distinguish from intraspecific variance without a careful design.

  5. 5.

    These standardised metrics are unbounded and follow approximately normal distributions. However, note that the correlation coefficient r is bounded at −1 and 1 and does not follow a normal distribution.

  6. 6.

    In a typical non-phylogenetic meta-analysis, a unit of analysis is ‘study’ where one effect size is taken from one study. Here, we assume that one effect size from each species comes from one study or \( n_{\text{effect}} = n_{\text{species}} = n_{\text{study}} \).

  7. 7.

    However, the penalised quasi-likelihood used in ASReml has been shown to largely underestimate the variance components for binary traits (Gilmour et al. 2006; de Villemereuil et al. 2013).

  8. 8.

    Note, however, that e in Eq. 11.14 should be considered as the effect due to additive dispersion rather than the residuals (for additive dispersion, see Nakagawa and Schielzeth 2010).

  9. 9.

    The data augmentation of Sect. 11.3.2, though, is very much linked to the MCMC algorithm.

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Acknowledgments

We are grateful for S. Lavergne, M. Lagisz, L. Z. Garamszegi and two anonymous reviewers for their comments on our earlier versions of this chapter; their comments have significantly improved this chapter. S.N. is supported by the Rutherford Discovery Fellowship (New Zealand).

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Authors and Affiliations

  1. Laboratoire d’Écologie Alpine (LECA-UMR CNRS 5553), Université Joseph Fourier, BP 53, 38041, Grenoble, France

    Pierre de Villemereuil

  2. Department of Zoology, University of Otago, 340 Great King Street, Dunedin, 9054, New Zealand

    Shinichi Nakagawa

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  1. Pierre de Villemereuil
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  2. Shinichi Nakagawa
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Correspondence to Pierre de Villemereuil .

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  1. Department of Evolutionary Ecology, Estación Biológica de Doñana-CSIC, Sevilla, Spain

    László Zsolt Garamszegi

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de Villemereuil, P., Nakagawa, S. (2014). General Quantitative Genetic Methods for Comparative Biology. In: Garamszegi, L. (eds) Modern Phylogenetic Comparative Methods and Their Application in Evolutionary Biology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43550-2_11

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